## MA40050: Numerical optimisation and large-scale systems

[Page last updated: 23 October 2023]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 2
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20218 AND take MA20222
Learning Outcomes: Students should know a range of modern iterative methods for solving nonlinear systems and optimisation problems. They should be able to analyse their algorithms and should have an understanding of relevant practical issues and their importance in a range of application areas.

Aims: To teach an understanding of iterative methods for nonlinear equations and optimisation.

Skills: Problem Solving (T,F&A), Computing (T,F&A), independent study and report writing.

Content: Topics will be chosen from the following:
Solution methods for nonlinear equations: Newton's method. Computation of solution paths. Pseudo-arc length continuation.
Unconstrained Optimisation: Line search vs trust region methods. Quasi-Newton and nonlinear conjugate gradient. Linear and nonlinear least squares.
Constrained Optimisation: Optimality conditions, KKT systems, numerical methods for constrained optimisation, linear and nonlinear programming.
Large-scale systems: A motivating example from PDE-constrained optimisation. Reduced-order models (e.g., SVD-based methods) and sparse linear systems (e.g., iterative methods and preconditioners).

Course availability:

#### MA40050 is Optional on the following courses:

Department of Computer Science
• USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
• USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
• USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
• USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
• USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
• USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 3)
• USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
• USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 3)
• USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Mathematical Sciences
• RSMA-AFM16 : Integrated PhD Statistical Applied Mathematics
• TSMA-AFM17 : MRes Statistical Applied Mathematics
• TSMA-AFM19 : MSc Mathematics with Data Science for Industry
• TSMA-AWM19 : MSc Mathematics with Data Science for Industry
• TSMA-AFM16 : MSc Statistical Applied Mathematics
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

 Notes: This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24. Courses and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.